Multilevel and multistage optimization problems are closely-related classes in which multiple (possibly competing) DMs act at multiple points in time. The two classes include both game theoretic (multilevel) models, in which multiple decision-makers with competing objectives make decisions sequentially; and recourse (multistage) models, in which a single decision-maker must make a sequence of decisions over time in order to react to changing conditions. In this talk, we discuss algorithms for these two classes of related problems, focusing on the case of two-stage linear models in which there are discrete variables at the second-stage.